Gagliardi lives in northern New York in the picturesque Saint Lawrence River Valley with his wife Robin, and children Zachary, Michael, and Eric.ġ.1 Systems of Linear Equations 2 Exercise Set 1.1 12 1.2 Matrices and Elementary Row Operations 14 Exercise Set 1.2 23 1.3 Matrix Algebra 26 Exercise Set 1.3 37 1.4 The Inverse of a Square Matrix 39 Exercise Set 1.4 45 1.5 Matrix Equations 48 Exercise Set 1.5 51 1.6 Determinants 54 Exercise Set 1.6 65 1.7 Elementary Matrices and LU Factorization 68 Exercise Set 1.7 77 1.8 Applications of Systems of Linear Equations 79 Exercise Set 1.8 84 Review Exercises 89 Chapter Test 90 CHAPTER Gagliardi is an accomplished double bassist and has recently recorded a CD of jazz standards with Author/Pianist Bill Vitek. In addition to his work as a mathematician, Dr. His focus there is on the graphical realization of certain types of sequences. Gagliardi also does research in Graph Theory. In particular, his current work is concerned with developing algorithmic formulations to describe the fine structure (characters and Weyl groups) of local symmetric spaces. Gagliardi’s principle area of research is in Symmetric Spaces. in Pure Mathematics from North Carolina State University in 2003 under the supervision of Aloysius Helminck.
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Gagliardi began his career as a software engineer at IBM in East Fishkill New York writing programs to support semiconductor development and manufacturing.
Daniel Gagliardi is an Assistant Professor of Mathematics at SUNY Canton, in Canton New York. Jim and his wife Regan live outside of Canton New York in a 150 year old farm house. Jim is married and has two children David and Sara. DeFranza has also published a dozen research articles in the areas of Sequence Spaces and Classical Summability Theory. DeFranza has coauthored PRECALCULUS, Fourth Edition and two other texts in single variable and multivariable calculus. in Pure Mathematics from Kent State University in 1979. It is this many years of working closely with students that has shaped this text in Linear Algebra and the other texts he has written. Lawrence University is a small Liberal Arts College in upstate New York that prides itself in the close interaction that exists between students and faculty.
Lawrence University in Canton New York where he has taught undergraduate mathematics for 25 years. Jim DeFranza is Professor of Mathematics at St. Jim DeFranza was born in 1950 in Yonkers New York and grew up in Dobbs Ferry New York on the Hudson River. To Regan, Sara, and David -JD To Robin, Zachary, Michael, and Eric -DG Algebras, Linear-Problems, exercises, etc. Donnelly Crawfordsville, IN Library of Congress Cataloging-in-Publication Data DeFranza, James, 1950– Introduction to linear algebra / James DeFranza, Daniel Gagliardi. Leick Compositor: Laserwords Private Limited Typeface: 10.25/12 Times Printer: R. Janssen Cover Designer: Ron Bissell (USE) Cover Image: Royalty-Free/CORBIS Senior Photo Research Coordinator: John C.
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No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Copyright © 2009 by The McGraw-Hill Companies, Inc. INTRODUCTION TO LINEAR ALGEBRA WITH APPLICATIONS Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. INTRODUCTION TO LINEAR ALGEBRA WITH APPLICATIONS CHAPTER 1 Systems of Linear Equations and Matricesġ.2 Matrices and Elementary Row Operationsġ.7 Elementary Matrices and LU Factorizationġ.8 Applications of Systems of Linear EquationsĬHAPTER 2 Linear Combinations and Linear IndependenceĤ.4 Matrix Representation of a Linear Transformationĥ.3 Application: Systems of Linear Differential EquationsĦ.5 Application: Least Squares ApproximationĦ.6 Diagonalization of Symmetric MatricesĦ.8 Application: Singular Value Decomposition
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